We have isolated a large number of polynucleotide kinase ribozymes from a pool of RNA molecules consisting of an ATP-binding domain flanked by regions of random sequence. Different classes of kinases catalyse the transfer of the gamma-thiophosphate of ATP-gamma S to the 5’-hydroxyl or to internal 2’-hydroxyls. An engineered version of one class is able to catalyse the transfer of thiophosphate from ATP-gamma S to the 5’-hydroxyl of an exogenous oligoribonucleotide substrate with multiple turnover, thus acting as a true enzyme.